Subgroups — C₁₂₇×#21375 #44585048

Order 32512.

1226 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₂₇×#1984	C₂	1	2	yes	maximal, complemented
5	C₁₂₇×#1954	C₂	1	2	yes	maximal, complemented
6	C₁₂₇×#1869	C₂	1	4	yes	maximal, complemented
7	C₁₂₇×#1750	C₂	1	4	yes	maximal, complemented
8	C₂³×C₈×C₁₂₇	C₂²	1	2	yes	—
9	#529×C₁₂₇	—	2	4	no	—
10	#529×C₁₂₇	—	2	4	no	—
11	C₂×#126×C₁₂₇	C₄	1	2	yes	—
12	C₂×#125×C₁₂₇	C₄	1	1	yes	characteristic
13	C₂×#124×C₁₂₇	C₄	1	1	yes	characteristic
14	C₂×#123×C₁₂₇	C₄	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₁₂₇	C₄	1	1	yes	characteristic
16	C₂×#121×C₁₂₇	C₄	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₂₇	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₂₇	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
22	#432×C₁₂₇	—	2	4	no	—
23	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	8	yes	—
26	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₂₇	—	2	4	no	—
28	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
30	#336×C₁₂₇	C₂²	1	8	yes	—
31	C₂²×Q₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₂₇	C₂×C₄	1	2	yes	—
33	C₂²×D₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₂₇	—	2	4	no	—
39	C₂²×C₈×C₁₂₇	—	2	8	no	—
40	C₂²×C₈×C₁₂₇	C₂³	1	4	yes	—
41	C₂²×C₈×C₁₂₇	C₂³	1	4	yes	—
42	#126×C₁₂₇	—	2	8	no	—
43	#125×C₁₂₇	—	2	4	no	—
44	#124×C₁₂₇	—	2	4	no	—
45	#123×C₁₂₇	—	2	8	no	—
46	C₂²⋊Q₈×C₁₂₇	—	2	4	no	—
47	#121×C₁₂₇	—	2	4	no	—
48	C₄×Q₈×C₁₂₇	—	2	2	no	—
49	C₄×Q₈×C₁₂₇	—	2	2	no	—
50	C₄×D₄×C₁₂₇	—	2	4	no	—
51	C₄×D₄×C₁₂₇	—	2	4	no	—
52	C₄×D₄×C₁₂₇	—	2	2	no	—
53	C₄×D₄×C₁₂₇	—	2	2	no	—
54	#117×C₁₂₇	—	2	4	no	—
55	#117×C₁₂₇	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₂₇	D₄	1	4	yes	—
70	C₂×C₄²×C₁₂₇	D₄	1	4	yes	—
71	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₁₂₇	—	2	4	no	—
75	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
76	C₂²⋊C₈×C₁₂₇	—	2	16	no	—
77	#97×C₁₂₇	—	2	4	no	—
78	C₄×C₈×C₁₂₇	—	2	4	no	—
79	C₄×C₈×C₁₂₇	—	2	4	no	—
80	C₂⁴×C₁₂₇	C₂²×C₄	1	2	yes	—
81	C₂⁴×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
82	C₂×Q₈×C₁₂₇	—	2	2	no	—
83	C₂×Q₈×C₁₂₇	—	2	4	no	—
84	C₂×D₄×C₁₂₇	—	2	4	no	—
85	C₂×D₄×C₁₂₇	—	2	8	no	—
86	C₂×D₄×C₁₂₇	—	2	2	no	—
87	C₂×D₄×C₁₂₇	—	2	4	no	—
88	C₂²×C₄×C₁₂₇	—	2	4	no	—
89	C₂²×C₄×C₁₂₇	—	2	4	no	—
90	C₂²×C₄×C₁₂₇	—	2	4	no	—
91	C₂²×C₄×C₁₂₇	—	2	2	no	—
92	C₂²×C₄×C₁₂₇	—	2	2	no	—
93	C₂²×C₄×C₁₂₇	—	2	8	no	—
94	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	4	yes	—
95	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₁₂₇	—	2	16	no	—
108	C₂×C₈×C₁₂₇	—	2	4	no	—
109	C₂×C₈×C₁₂₇	—	2	4	no	—
110	C₂×C₈×C₁₂₇	—	2	4	no	—
111	C₂×C₈×C₁₂₇	—	2	8	no	—
112	C₂×C₈×C₁₂₇	#41	1	8	yes	—
113	C₄⋊C₄×C₁₂₇	—	2	4	no	—
114	C₄⋊C₄×C₁₂₇	—	2	4	no	—
115	C₄⋊C₄×C₁₂₇	—	2	2	no	—
116	C₄⋊C₄×C₁₂₇	—	2	4	no	—
117	C₄⋊C₄×C₁₂₇	—	2	2	no	—
118	C₄⋊C₄×C₁₂₇	—	2	4	no	—
119	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
120	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
121	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
122	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
123	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
124	C₄²×C₁₂₇	—	2	2	no	—
125	C₄²×C₁₂₇	—	2	2	no	—
126	C₄²×C₁₂₇	C₂²⋊C₄	1	4	yes	—
127	C₄²×C₁₂₇	C₂²⋊C₄	1	4	yes	—
128	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
129	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
130	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
131	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
132	C₂³×C₁₂₇	—	2	2	no	—
133	C₂³×C₁₂₇	—	2	2	no	—
134	C₂³×C₁₂₇	—	2	2	no	—
135	C₂³×C₁₂₇	—	2	4	no	—
136	C₂³×C₁₂₇	—	2	4	no	—
137	C₂³×C₁₂₇	—	2	4	no	—
138	C₂³×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂³×C₁₂₇	#131	1	4	yes	—
140	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
141	Q₈×C₁₂₇	—	4	4	no	—
142	D₄×C₁₂₇	—	4	8	no	—
143	D₄×C₁₂₇	—	4	4	no	—
144	C₂×C₄×C₁₂₇	—	2	2	no	—
145	C₂×C₄×C₁₂₇	—	2	2	no	—
146	C₂×C₄×C₁₂₇	—	2	2	no	—
147	C₂×C₄×C₁₂₇	—	2	2	no	—
148	C₂×C₄×C₁₂₇	—	2	8	no	—
149	C₂×C₄×C₁₂₇	—	2	4	no	—
150	C₂×C₄×C₁₂₇	—	2	4	no	—
151	C₂×C₄×C₁₂₇	—	2	8	no	—
152	C₂×C₄×C₁₂₇	—	2	2	no	—
153	C₂×C₄×C₁₂₇	—	2	2	no	—
154	C₂×C₄×C₁₂₇	—	2	2	no	—
155	C₂×C₄×C₁₂₇	—	2	4	no	—
156	C₂×C₄×C₁₂₇	—	2	4	no	—
157	C₂×C₄×C₁₂₇	—	2	4	no	—
158	C₂×C₄×C₁₂₇	—	4	4	no	—
159	C₂×C₄×C₁₂₇	—	4	4	no	—
160	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₂₇	#131	1	4	yes	—
166	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₂₇	C₂×#41	1	4	yes	—
169	C₈×C₁₂₇	—	2	8	no	—
170	C₈×C₁₂₇	—	4	4	no	—
171	C₂²×C₁₂₇	—	2	2	no	—
172	C₂²×C₁₂₇	—	2	8	no	—
173	C₂²×C₁₂₇	—	2	2	no	—
174	C₂²×C₁₂₇	—	4	2	no	—
175	C₂²×C₁₂₇	—	4	2	no	—
176	C₂²×C₁₂₇	—	4	8	no	—
177	C₂²×C₁₂₇	—	4	2	no	—
178	C₂²×C₁₂₇	#408	1	4	yes	—
179	C₂²×C₁₂₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₁₂₇	C₄×#41	1	2	yes	—
181	C₂²×C₁₂₇	C₂×#131	1	2	yes	—
182	C₂²×C₁₂₇	C₂×#131	1	2	yes	—
183	C₄×C₁₂₇	—	2	2	no	—
184	C₄×C₁₂₇	—	2	2	no	—
185	C₄×C₁₂₇	—	2	2	no	—
186	C₄×C₁₂₇	—	2	2	no	—
187	C₄×C₁₂₇	—	4	2	no	—
188	C₄×C₁₂₇	—	4	2	no	—
189	C₄×C₁₂₇	—	4	2	no	—
190	C₄×C₁₂₇	#408	1	4	yes	—
191	C₄×C₁₂₇	#525	1	2	yes	—
192	C₄×C₁₂₇	#532	1	2	yes	—
193	#21375	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂×C₁₂₇	—	2	4	no	—
195	C₂×C₁₂₇	—	8	2	no	—
196	C₂×C₁₂₇	#2297	1	1	yes	characteristic
197	C₂×C₁₂₇	C₂×#408	1	1	yes	characteristic
198	C₂×C₁₂₇	C₂×#408	1	1	yes	characteristic
199	C₂×C₁₂₇	#2966	1	4	yes	—
200	C₂×#529	C₂×C₁₂₇	1	1	yes	characteristic
201	C₂×#432	C₂×C₁₂₇	1	1	yes	characteristic, complemented
202	C₂²×C₄×C₈	C₂×C₁₂₇	1	1	yes	characteristic, complemented
203	#1984	C₂×C₁₂₇	1	2	yes	complemented
204	#1954	C₂×C₁₂₇	1	2	yes	complemented
205	#1869	C₂×C₁₂₇	1	4	yes	complemented
206	#1750	C₂×C₁₂₇	1	4	yes	complemented
207	C₁₂₇	#21375	1	1	yes	characteristic, direct product factor, Sylow
208	C₂³×C₈	C₂²×C₁₂₇	1	2	yes	—
209	#529	—	2	4	no	—
210	#529	—	2	4	no	—
211	C₂×#126	C₄×C₁₂₇	1	2	yes	—
212	C₂×#125	C₄×C₁₂₇	1	1	yes	characteristic
213	C₂×#124	C₄×C₁₂₇	1	1	yes	characteristic
214	C₂×#123	C₄×C₁₂₇	1	2	yes	—
215	C₂×C₂²⋊Q₈	C₄×C₁₂₇	1	1	yes	characteristic
216	C₂×#121	C₄×C₁₂₇	1	1	yes	characteristic
217	C₂×C₄×Q₈	C₂²×C₁₂₇	1	1	yes	characteristic
218	C₂×C₄×D₄	C₂²×C₁₂₇	1	2	yes	—
219	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
220	C₂×#117	C₂²×C₁₂₇	1	2	yes	—
221	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
222	#432	—	2	4	no	—
223	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
225	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	8	yes	—
226	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
227	C₂×C₄×C₈	—	2	4	no	—
228	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
229	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
230	#336	C₂²×C₁₂₇	1	8	yes	—
231	C₂²×Q₈	C₂×C₄×C₁₂₇	1	1	yes	characteristic
232	C₂²×D₄	C₂×C₄×C₁₂₇	1	2	yes	—
233	C₂²×D₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
234	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
235	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
237	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
238	C₂²×C₈	—	2	4	no	—
239	C₂²×C₈	—	2	8	no	—
240	C₂²×C₈	C₂³×C₁₂₇	1	4	yes	—
241	C₂²×C₈	C₂³×C₁₂₇	1	4	yes	—
242	#126	—	2	8	no	—
243	#125	—	2	4	no	—
244	#124	—	2	4	no	—
245	#123	—	2	8	no	—
246	C₂²⋊Q₈	—	2	4	no	—
247	#121	—	2	4	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×D₄	—	2	4	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	#117	—	2	4	no	—
255	#117	—	2	4	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
267	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
268	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
269	C₂×C₄²	D₄×C₁₂₇	1	4	yes	—
270	C₂×C₄²	D₄×C₁₂₇	1	4	yes	—
271	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
272	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
274	C₄⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	C₂²⋊C₈	—	2	16	no	—
277	#97	—	2	4	no	—
278	C₄×C₈	—	2	4	no	—
279	C₄×C₈	—	2	4	no	—
280	C₂⁴	C₂²×C₄×C₁₂₇	1	2	yes	—
281	C₂⁴	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	4	yes	—
295	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	4	yes	—
296	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
307	C₂×C₈	—	2	16	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	8	no	—
312	C₂×C₈	#41×C₁₂₇	1	8	yes	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	C₂²⋊C₄×C₁₂₇	1	4	yes	—
327	C₄²	C₂²⋊C₄×C₁₂₇	1	4	yes	—
328	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
329	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
330	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
331	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	4	no	—
338	C₂³	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
339	C₂³	#131×C₁₂₇	1	4	yes	—
340	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
341	Q₈	—	4	4	no	—
342	D₄	—	4	8	no	—
343	D₄	—	4	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
365	C₂×C₄	#131×C₁₂₇	1	4	yes	—
366	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
367	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₁₂₇	1	4	yes	—
369	C₈	—	2	8	no	—
370	C₈	—	4	4	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	8	no	—
377	C₂²	—	4	2	no	—
378	C₂²	#408×C₁₂₇	1	4	yes	—
379	C₂²	C₂²×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
380	C₂²	C₄×#41×C₁₂₇	1	2	yes	—
381	C₂²	C₂×#131×C₁₂₇	1	2	yes	—
382	C₂²	C₂×#131×C₁₂₇	1	2	yes	—
383	C₄	—	2	2	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	#408×C₁₂₇	1	4	yes	—
391	C₄	#525×C₁₂₇	1	2	yes	—
392	C₄	#532×C₁₂₇	1	2	yes	—
393	C₂	—	2	4	no	—
394	C₂	—	8	2	no	—
395	C₂	C₁₂₇×#2297	1	1	yes	characteristic
396	C₂	C₂×#408×C₁₂₇	1	1	yes	characteristic
397	C₂	C₂×#408×C₁₂₇	1	1	yes	characteristic
398	C₂	C₁₂₇×#2966	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₂₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂³×C₁₂₇	C₂³×C₄
prime radical	C₂×#121×C₁₂₇	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₂₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#432×C₁₂₇	C₂	semidirect
3. C₂²×C₄×C₈×C₁₂₇	C₂	semidirect
4. C₁₂₇×#1984	C₂	semidirect
5. C₁₂₇×#1954	C₂	semidirect
6. C₁₂₇×#1869	C₂	semidirect
7. C₁₂₇×#1750	C₂	semidirect
193. #21375	C₁₂₇	direct (N × H)
201. C₂×#432	C₂×C₁₂₇	semidirect
202. C₂²×C₄×C₈	C₂×C₁₂₇	semidirect
203. #1984	C₂×C₁₂₇	semidirect
204. #1954	C₂×C₁₂₇	semidirect
205. #1869	C₂×C₁₂₇	semidirect
206. #1750	C₂×C₁₂₇	semidirect
207. C₁₂₇	#21375	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#529×C₁₂₇	2
C₂×#432×C₁₂₇	2
C₂²×C₄×C₈×C₁₂₇	2
C₁₂₇×#1984	2
C₁₂₇×#1954	2
C₁₂₇×#1869	2
C₁₂₇×#1750	2
#21375	127

Subgroups — C127×#21375 #44585048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21375 #44585048